Yes, it changs the freefall time. 4000+ feet on the top adds about 18-20 seconds more to the skydive. Some planes take so long in climbing above 10,000 feet that the operator finds that the jumpers just do not want to wait another 10 minutes to get 2000 feet or it costs more in fuel then its worth. Planes such as Cessna 182's and 206's are usually operated at 10k or less since with a full load (4-5 people) the climb time to 10k is already 20-25 minutes and to get to 14k might take 30-40 minutes. Turbine aircraft (8-22 people) usually do not have the same issues and operate up to much higher altitudes for skydiving operations.

It also depends on the MSL. Taking off from 150 MSL is different than going from 5000 MSL. The aircraft performance is degraded and getting those last few k of altitude not only takes longer but everyone in the plane starts passing out...